This thesis is focused on protecting sensitive data in optimization-based control methods. We propose a novel Privacy-preserving Model Predictive Controller (PMPC) where multiple agents are controlled by an untrusted external coordinator. By using the Paillier additively Homomorphic Encryption (HE) scheme, our PMPC allows the coordinator to solve a Quadratic Programming (QP) problem over encrypted data. The PMPC is based on a Projected Gradient Scheme (PGS) on the Lagrange-dual, which enables the use of quadratic cost functions with complicated constraints (e.g., constraints on linear combinations of states and inputs). Compared to the state-of-the-art, the proposed controller protects not only the states and inputs of the agents, but also the system models, cost function and constraints.

Optimization problems with quadratic cost functions and linear constraints, form the basis of a wide class of Model Predictive Control (MPC) problems. Examples of applications are smart-grids, large industrial plants and robotics. To test our PMPC, we focus on the application in self-driving vehicles. Motivated by the AUTOTRAC 2020 competition, we formulate a controller for multiple vehicles in a platoon. An external coordinator controls the longitudinal velocities of up to ten vehicles, while complicated constraints on the positions prevent collisions. By using our PMPC, the external coordinator does not gain access to the private data of the vehicles, protecting their privacy. Because of the wide application domain of MPC, we would like to extend this research in the future by testing the PMPC on other applications as well.